Our FREE site is mostly funded by the Amazon ads ⇓below⇓.

Support us by clicking ⇑above⇑ next time you plan to buy a product on Amazon.

"""
Problem Statement:
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
"""
def solution(n):
"""
Return the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
>>> solution(1000)
31875000
"""
product = -1
d = 0
for a in range(1, n // 3):
"""Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
"""
b = (n * n - 2 * a * n) // (2 * n - 2 * a)
c = n - a - b
if c * c == (a * a + b * b):
d = a * b * c
if d >= product:
product = d
return product
if __name__ == "__main__":
print(solution(int(input().strip())))